Private companies should be allowed to take over the running of state schools, the outgoing chairman of Ofsted has said.

Zenna Atkins praised the Government's free schools policy, which allows parents and charities to run state schools, but urged ministers to go further by extending that right to profitmaking firms.

In an interview with The Sunday Telegraph, Miss Atkins, who has left her job to run the British arm of GEMS Education, an independent schools chain, said that state schools could also improve exam results and save money by learning new techniques from the private sector.

It came as figures from the Department for Education showed that academies, many of which have corporate sponsors, improved their performance at three times the national average in last week's GCSE results.

Academies, which the Coalition plan to expand greatly in number, reported a seven per cent increase in the number of pupils gaining five GCSEs at grades A* to C, including English and maths, compared with the national average of 2.5 per cent.

Miss Atkins said: "At the moment the constraining factor is the fact that academies, free schools and schools that are state funded need to be run by charitable trusts or by the state itself and I think there is an opportunity to expand and look at the role that the private sector can play.

"Currently the private sector, if you're running a school, has to set up a charitable vehicle to do that and that seems to be an unnecessary level of bureaucracy.

"A lot of countries are trying to open up the market so that increasing numbers of schools operators can get involved in the delivery of schools.

"At the moment in the UK that is being opened up with quite a progressive policy by Michael Gove (the Education Secretary) and his team but I think that doesn't necessarily need to stop with the charitable sector."

Miss Atkins said the Coalition's free schools, which will be free from local authority control, would benefit from the help of private companies.

"It's a daunting thing for a group of parents and they will need support and assistance in doing that," she said.

"The Government can offer a lot of practical guidance and support going through the process. They don't offer the practical guidance and support in how you actually run the school.

"I think parents are looking for a greater degree of support in that."

She added: "Schools tend not to be run in a businesslike fashion. And that is everything from the management information to basic systems, processes, back office."

Using better systems could help more children pass exams with improved grades, she said, and finances in the education sector could also benefit from corporate expertise.

She insisted that new school premises could be constructed from existing funds despite Mr Gove's decision to scrap 715 projects in the building programme which was known as Building Schools for the Future.

"I think it's perfectly possible within existing funding formulas to run schools more efficiently. Therefore, you can afford to service capital and you can afford the school that you aspired to get while Building Schools for the Future existed," she said.

Miss Atkins also insisted she was unaware of the phenomenon of parents who opportunistically begin attending church in order to win places for their children at oversubscribed church-run schools.

The practice has even led the Church of England to introduce a system to evaluate how often parents worship, to help prioritise admissions.

Asked if she had a view on the trend, Miss Atkins said: "As far as I'm aware Ofsted haven't got any subject matter that shows that has happened.

"You are probably better qualified about it than I am."

Her remarks come despite evidence from different denominations about parents joining congregations in a bid to secure school places.

Cardinal Cormac Murphy-O'Connor, the then Archbishop of Westminster and leader of the 4.5 million Catholics in England and Wales, told this newspaper in 2008 that he did not condemn parents who misrepresented their religion.

"I wouldn't want to judge parents who pretend to have a faith to get their children into school," he said.

"They'd do anything for the good of their children."

In 2007, the numbers of families doing so led the Church of England to set out three tiers which describe a prospective parent's relationship with the sponsoring church.

Families who worshipped twice a month would be regarded as "at the heart of the church" and therefore their children may be more likely to be awarded priority places.

Less frequent worship would lead to an applicant being regarded as "attached to the church" or "known to the church", the guidance said.

Earlier this year Miss Atkins courted controversy by recommending that "every school should have a useless teacher".